Associative Property & Identity Property

The basic Number Properties (or laws) that apply to arithmetic operations are Commutative Property,
Associative Property, Identity Property and Distributive Property. In this lesson, we will learn the
associative property and identity property of numbers.

Summary of Number Properties

The following table summarizes the number properties for addition and multiplication: Commutative, Associative and Identity. Scroll down the page for more examples, explanations and solutions.

Associative Property

The associative property states that the sum or product of a set of numbers is the same, no matter how the numbers are grouped.
An operation is associative if a change in grouping does not change the results. This means the parenthesis (or brackets) can be moved.

Numbers that are added can be grouped in any order.

For example:

(4 + 5) + 6 = 5 + (4 + 6)

(x + y) + z = x + (y + z)

Numbers that are multiplied can be grouped in any order.

For example:

(4 × 5) × 6 = 5 × (4 × 6)

(x × y) × z = x × (y × z)

Numbers that are subtracted are NOT associative.

For example:

(4 – 5) – 6 ≠ 5 – (4 – 6)

(x – y) – z ≠ x – (y – z)

Numbers that are divided are NOT associative.

For example:

(4 ÷ 5) ÷ 6 ≠ 5 ÷ (4 ÷ 6)

(x ÷ y ) ÷ z ≠ y ÷ ( x ÷ z)

What is the Associative Property?

The following video explains: What is the associative property? Why does it have the name it does?
How can you recognize it when you see it? How can you distinguish it from other situations that look very similar?

Identity Property

What is the identity property? How can you recognize it and name it when you see it? Why does is have the name it has? Why do mathematicians give EVERYTHING, even something as seemingly simple as this a name?

Multiplication: Zero Property

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